Those who attack works of art are not, in one sense, wrong. You don't assault something you are indifferent to, or something that doesn't threaten you; iconoclasts rarely smash images out of apathy. Take the man who raised his walking-stick against Manet's Music in the Tuileries Gardens when it formed part of a one-man show at the Galerie Martinet in 1863. The assailant left no account of his motives, but the picture's offence would surely have come under the heading of fraud: it was a masquerade, something that insulted not just him, the viewer, but the entire history of art, on whose behalf he was obliged to speak – or rather, act. Further, the painting's very subject-matter – a swath of contemporary Parisian life – would have been objectionable. This now seems ironic, since the painting was in fact about the sort of man who had attacked it, and the sort of life he and his friends then lived in Paris. Manet was saying: here, now, as it is.

When Napoleon III saw Le déjeuner sur l'herbe at the Salon des Refusés in 1863, he said it was "an offence against decency"; while his consort, the Empress Eugenie, pretended the picture did not exist. (Nowadays, this would be brilliant publicity; then, it was a disaster, as the Salon des Refusés was closed down and independent painters had no large public space to exhibit in for the next 20 years.) When Olympia was shown at the Salon of 1865, physical threats meant it had to be rehung above the doorway of the last gallery, so high that it was hard to tell "whether you were looking at a parcel of nude flesh or a bundle of laundry". Such imperial and public disapproval ensured that for much of his career Manet also had to put up with the sneers and sarcasms of the popular press. Again, they were not wrong, in the sense that their feeling was authentic: contempt rooted in unacknowledgeable fear. What they dreaded was perfectly clear to one of the most cultured and sophisticated loathers of Manet: Edmond de Goncourt. "A joke, a joke, a joke!" he shouted into his diary after seeing the posthumous Manet exhibition of January 1884. But he recognised that the joke had long turned serious, and was on him and his kind:

With Manet, whose techniques are lifted from Goya, with Manet and all the painters who have followed him, what we have is the death of oil painting, that's to say, of painting with a pretty, amber, crystalline transparency, of which Rubens's Woman in a Straw Hat is the epitome. Now we have opaque painting, matt painting, chalky painting, painting with all the characteristics of furniture paint. And everyone's doing it like that, from Raffaelli to the last little Impressionist dauber.

Even those who were on Manet's side knew that you cannot have the arrival of something new without the death of something old. So Baudelaire, while hailing him as (possibly) the painter of modern life the age demanded – although the poet-critic judged Constantin Guys the real thing – wrote to Manet: "You are only the first in the degeneration of your art." As Anita Brookner acutely commented: "Does he sense in Manet the inception of art without a moral dimension?"

Ezra Pound said that he would throw the brick through the window, while Eliot went round the back and grabbed the swag; and so it proved. And there's a sense in which Manet threw the brick and the Impressionists grabbed the swag: certainly if swag is measured in blockbuster exhibitions a century and more on. But now Manet has a semi-blockbuster of his own – 186 items against the traditional (and exhausting) three hundred or so – and Olympia has made her way from the Louvre to the Musée d'Orsay. Big Manet shows don't come along that often (the last one in Paris was in 1983), and it's important to be reminded every so often what he did to and for French art. He brightened and lightened its palette (where academicians began with dark tones and worked upwards to lighter ones, Manet's peinture claire did the opposite); he discarded half-tones and brought in a new transparency (he was against paintings that were "stews and gravies"); he simplified and emphasised outline; he frequently discarded traditional perspective (the bathing woman in Le déjeuner sur l'herbe is quite "wrong" – too large – in terms of the assumed distance); he compressed the depth of field, and pushed figures further out towards us (Zola said of paintings like The Fifer that "they break the wall"); he introduced "Manet black" and "Manet white". He also rejected large amounts of traditional subject-matter: mythology, allegory, history (his "history" paintings are all contemporary). "One must be of one's time and paint what one sees." He can be located by the triangulation of the three great writers who championed him: Baudelaire the dandy and poet of modern life; Zola the naturalist; Mallarmé the pure aesthete. Has any painter ever had such writerly support? Yet Manet was not in the least a literary or illustrative painter. His famous "literary" painting – of Zola's Nana – is not at all what it seems. He represented the courtesan when she was still only a minor figure in the serialisation of Zola's earlier novel L'Assommoir. Huysmans, in a review of the picture, announced that Zola was going to devote a whole novel to Nana, and congratulated Manet on having "shown her as she undoubtedly will be". So you could say it was Zola who "illustrated" Manet, rather than vice versa.

Much of Manet's achievement you can understand by reading the books and looking at the colour plates; much else is apparent only in front of the pictures themselves. "Manet black" reproduces fairly well; "Manet white" very poorly. Olympia, aside from its continuing erotic challenge, is also a Whistlerian "Symphony in Off-White" (subtle exchanges between flesh, coverlet, bedclothes, flowers and – the sharpest white of all – the paper in which the flowers are wrapped). In the portrait of Zola, a central patch of white blazes out: it comes, appropriately, from the pages of the book the novelist is reading. The tender portrait of Mme Manet, La Lecture, sets white dress against white sofa-covering against the greyer white of lace curtains. Even one of Manet's most radical – and most fearsomely ugly – portraits, of Baudelaire's mistress (tiny doll-head, enormous right mitt, plus improbable, possibly severed, right leg sticking out of frock) is, you suspect, mainly about the opportunity to fill the canvas from side to side with an enormous, billowing white dress. All this is to look at Manet in terms of what he can be seen, retrospectively, to have achieved. But painters often don't live to see what they have achieved. Further, painters have very varying trajectories: some, like Degas or Bonnard, follow a path it is easy for us to understand, and produce work of an almost scarily consistent quality. Others, like Manet, are much harder to follow; harder, perhaps, even for themselves to follow. One of the things the show at the Musée d'Orsay does is confirm what a restless, as well as what an uneven, painter Manet was. This truth emerges all the more clearly because of the new approach the show's curators have taken. Art moves on, and so does art history and museum theology. Nowadays, curators – unlike audiences – seem to hate shows which just line up one masterpiece after another, and which retell the same old story. Here, they call it, Frenchly, "simplifying his modernity to an iconographic register".

There is some point to this. Just as it's easy to forget how provoking Manet originally was, it's easy to forget how quickly the shock of the new becomes visually absorbed (and museumified, and commodified). Proust, in The Guermantes Way, describes how such appropriation can easily take place within a lifetime. His duchess goes on a visit to the Louvre:

and we happened to pass Manet's Olympia. Nowadays nobody is in the least surprised by it. It looks just like an Ingres! And yet, heaven knows how I had to take up the cudgels on behalf of that picture, which I don't altogether like but which is unquestionably the work of somebody.

So there is an obvious danger to the masterpieces-on-a-washing-line approach, which merely rehearses how art history settled down a hundred years ago: the risk being that we can no longer see, only take for granted. But where is the counter-narrative to be found? Currently, it is in historical and social context, in a rejection of those who have "vampirised" the painter "in the name of modern art". This leads – astonishingly – to a Manet who was "the upholder of traditional values". For instance, the "same old story" tells how the young Manet spent six years in the studio of Thomas Couture, a fashionable peintre-pompier, without learning anything from him. The d'Orsay show therefore opens with a roomful of Couture, encouraging us to conclude the opposite. It's true that one early Manet portrait closely resembles Couture. Yet the two most striking pictures in the room – a grave and melancholy study of his parents, and a small boy, Le Petit Lange, full of Manet black and with those intensely staring black Manet eyes – bear little influence of Couture; indeed, they demonstrate Manet getting away from his teacher's style as quickly as possible.

More bizarrely interesting is Manet's "Catholic" period, to which the exhibition devotes a whole room, and which will come as a great surprise to most people who think they know their Manet. Having established himself, and been roundly hissed for it, with Le déjeuner sur l'herbe (1862- 3) and Olympia (1863), Manet produced several religious paintings in 1864-5 – a massive dead Christ, a similarly massive Mocking of Christ, and a kneeling monk – which, as the catalogue has it, "revolted his enemies as much as they embarrassed his admirers". Manet's great friend Antonin Proust left them out of that posthumous show which Goncourt dismissed as a joke. Quite right too: they are the sort of derivative, academic monsters you nowadays see hung high up in provincial Musées des Beaux-Arts, long exiled there by a relieved Paris art bureaucracy ("Look, we are sending you a Manet!"). You can see why they form part of the curators' counter-narrative – these works did occupy a lot of the mature Manet's time; but equally, the counter-narrative seems to involve not so much the democratisation of value as its suspension. "A Suspect Catholicism" is the room's title. Better: "The Shock of the Bad".

Still, this room acts as a useful early warning. Manet was not always "Manet". There are a number of paintings on show which might well cause an upset in any artistic blind-tasting. For instance, a Whistlerish, Japanesy Bateaux en mer with a sail shaped like an oriental monogram (a typical Manet witticism), or the Boulogne beach-scene which is like a Boudin suddenly brought into crisp focus (also with some perspectival oddities, like an improbably giant male figure on the right). The first comes from Le Havre, the second from Richmond, Virginia. The curators have been diligent, and original. They have shown Manet to be a different painter from what one might lazily expect; but not a greater one. Manet's most famous paintings are rightly his most famous; they never fail, and still surprise. (For instance, I hadn't previously noticed that the naked figure in Le déjeuner has an almost imperceptible black ribbon in her hair: it's as if Manet is saying: "Nude – what nude? Can't you see she's wearing a ribbon?") The disappointment of the show is that if he painted, say, 12 (or 14, or 16) incontestable masterpieces, under half are present here: no Music in the Tuileries (which John Richardson has called "the first truly modern picture"), no Le chemin de fer, no Argenteuil, no Nana, no Le déjeuner dans l'atelier, no A Bar at the Folies-Bergères; the Boston Execution of the Emperor Maximilian but not the Mannheim one (or the Degas fragments); the lesser of the two pictures of Monet on his bateau-atelier; not the famous bunch of asparagus but the single extra one Manet painted and sent along as a "tip" after the buyer had generously overpaid. There may have been difficulties over loans, and the rooms at the d'Orsay are fairly cramped (though enormous space is given to another piece of empty pomp – Jean-Baptiste Faure singing the title role in Ambroise Thomas's Hamlet); but most likely, it is because the curators are determined to find, if not impose, a new narrative thread. At times they seem deliberately to mock our expectations. Thus there is a tiny copy of Le Chemin de fer – a photo embellished with watercolour and gouache – by Jules-Michel Godet. It's as if the curators are saying: you're missing one of your favourites? Have it like this, then.

So it is a risky show. There are some good surprises, like Baudelaire drawings and a collection of the dandyish, galant watercolour-letters Manet wrote (usually to women). The four black portraits of Berthe Morisot – the nearest he came to Impressionist series-painting – grow in force when lined up side by side (though again, the great portrait of her, the white Le repos, is absent). There are two pretty pastels of women, even if they remind us how Degas, who introduced Manet to the medium, used it better; these are hung in a roomful, a dream, of fair women – and yet my eye was most caught here by a less obviously seductive self-portrait by Mary Cassatt. And away from all the scuffle of argument and counter-narrative, there is a quiet space for still-lives. This genre accounted for one-fifth of Manet's entire output (not least because of the pictures' saleability). On a trip to Venice in 1875 with his wife Suzanne and fellow-painter Tissot, he announced – while standing in the fishmarket – that he wanted to be "the St Francis of still life". At the vegetable market he spotted a pile of Brenta pumpkins and cried out: "Turks heads in turbans! Trophies from the victories of Lepanto and Corfu." And on the same visit, he concluded: "A painter can say all he wants to with fruit, or flowers, or even clouds." In the still-life room at the Musée d'Orsay, two simple images held me: flowers in tall crystal vases, painted in 1882, the year before his death. Manet, the dandy, the happily married coureur de femmes, died (like Baudelaire) of tertiary syphilis. It was an atrocious end: locomotor ataxia, the wheel-chair, gangrene, an amputated leg, then death. In this last stretch of his life, Manet repeatedly painted the ephemeral beauty of flowers. As if he were quietly repeating the words the stick-wielder had refused to hear all those years previously, and saying one last time: yes, here, now, as it is.

Manet, the Man Who Invented Modern Art is at the Musée d'Orsay, Paris, until 3 July 2011.